A known and successful system for detecting small quantities of gas in the environment is by the use of absorption spectroscopy. By this technique, a light beam of selected wavelengths that are highly absorbed by the particular gas for which the instrumentation is designed to detect passes through a sample of the gas. The rate of absorption of the light beam is used as an indicator of the level of concentration of the gas in the same. In order to improve the sensitivity of detecting low levels of concentration of gas by spectral absorption, it is necessary to pass the light beam through a relatively long pathway of the gas sample. Stated another way, as the length of the light beam passing through a sample is increased, the sensitivity of the instrument to detect very small levels of gasses is also increased, since the absorption increases.
It is easy to understand that if a beam is passed through a very long tube containing a sample of gas that the instruments requiring such a long tube would be extremely cumbersome and therefore not easily portable. To overcome this problem, others have devised systems wherein a beam of light is repeatedly reflected between opposed mirrors to thereby extending the length of exposure of the beam to a gas sample in a way that the size of the instrument can be substantially reduced.
A typical absorption cell of this type is referred to as a “multipass cell” and comprises an elongated cylinder in which mirrors are disposed at opposite ends and light is introduced into the cells through a hole in one of the mirrors. These multipass cells necessarily avoid having the mirror bounce spot locations overlap, since scattered light from each spot can reflect into the overlapped spot's beam direction, causing an interference etalon fringe pattern. These cells also generally use concave mirror surfaces to refocus the beam on each bounce, preventing the laser beam from diverging over the long optical path.
FIG. 1 illustrates an exemplary prior art multipass cell arrangement 1, comprising a pair of mirrors 2, 3 which are separated by a predetermined spacing d to form an optical cavity. Mirrors 2, 3 each have the same radius of curvature in this example, and take the form of spherical mirrors with a point focus. In order to create a spot pattern, an incoming laser beam is introduced into the cavity at an off-axis orientation (i.e., off-axis with respect to the optical axis OA of arrangement 1). Referring to FIG. 1, an incoming laser beam I is shown as being provided by a laser source 5 and introduced in the system through a hole 4 formed in mirror 3. Incoming laser beam I then bounces multiple times between mirrors 2 and 3, ultimately exiting through hole 4, as shown, and entering a detector 6. This particular prior art embodiment is described as a “reentrant” configuration, since the output laser beam passes through the same aperture as the input beam.
An exemplary spot pattern formed by the bounces is also shown in FIG. 1. Obviously, by increasing the number of bounces (thus, the number of spots), the optical path length increases. For many arrangements, such as in trace gas sensing as noted above, it is preferred to utilize a relatively long optical path length (measured in meters, at times tens of mirrors) within a relatively small physical size (that is, a separation d which tends to be more on the order of centimeters). While increasing the spot density provides this desired result, it is also important to prevent overlap of the spots (which otherwise creates unwanted interference effects, fringe patterns and the like). Inasmuch as the prior art configurations typically utilize spherical members which create spot patterns that are either a single circular or single elliptical pattern in form, these cells are limited in the number of spots that can be formed before overlapping occurs.
There are various multipass cell configurations known in the art which do not overlap spots in a relatively dense pattern. These configurations generally take the form of either pure astigmatic cells or cylindrical mirror-based multipass cells, rather than using the conventional spherical mirrors. The mirrors for pure astigmatic cells must be machined to extremely high tolerances to achieve the correct amount of astigmatism (thereby increasing overall system cost), and mismatched mirrors require rotation of one of the mirrors to provide the desired reentrant condition (i.e., matching of input and output beam locations for maximum stability, as described in U.S. Pat. No. 5,291,265, discussed below). The astigmatic cell was first described in the article “Off-axis paths in spherical mirror interferometers” by D. Herriott et al., appearing in Applied Optics, Vol. 3, page 523 et seq., 1964. A significant problem with the use of the astigmatic configuration is the high cost of extreme-precision tolerance mirrors with exact focal lengths to achieve a stable, predictable reentrant pattern. An alternative to the precision tolerance ground mirrors is to use a spherical mirror with compressing stress along one axis to bend the mirror and achieve an astigmatic mirror; however, this is not a stable configuration. Improvements to the development of such cells using relaxed tolerance astigmatic mirrors have been developed by Aerodyne Research, Inc., as disclosed in U.S. Pat. No. 5,291,265 issued to P. L. Kebabian on Mar. 1, 1994, which utilizes a pair of mirrors that are fabricated so that the ratios of their radii of curvature are actually larger than the values calculated from simulations. This improvement allows for the rotation of the mirrors about their axes to achieve the reentrant condition, enabling the use of lower tolerance mirrors. These cells produce a Lissajous pattern that only fill a diamond-shaped area on the mirror, wasting space around the periphery of the circular mirrors.
The cylindrical mirror-based multipass cells (where at least one mirror is cylindrical) provide the same astigmatic configuration of spots and are lower cost. However, the cylindrical patterns do not refocus the beam in both vertical and horizontal directions for each mirror bounce and, therefore, are more difficult to align and achieve the pattern density required for very high bounce number applications. A recent type of astigmatic cell using cylindrical mirrors is described in U.S. Pat. No. 7,307,716 entitled “Near Reentrant Dense Pattern Optical Multipass Cell” and issued to J. A. Silver on Dec. 11, 2007. Cylindrical mirrors are typically ground with a poorer precision surface quality (λ), which can cause scattering of the optical beam, leading to increased fringing when compared to off-the-shelf spherical mirrors that are ground at better than λ/4, and frequently λ/8. As with the above-cited Kebabian configuration, this cylindrical-based design also produces a Lissajous pattern (which wastes space on the mirror surface).
One of the newer types of multipass cell utilizes a specially-designed spherical mirror-based arrangement, utilizing a “split spherical mirror” as one termination, as described in the article “Simple, stable and compact multiple-reflection optical cell for very long optical paths” by C. Robert and appearing in Applied Optics, Vol. 46, No. 22, August 2007, p. 5408 et seq. While providing an increase in spot density (and, as a result, optical path length), this type of cell causes the spot pattern to spiral into the center and presents some beam quality issues, since the beam traversing the spot pattern does not reflect on symmetric surfaces, causing major skew of the beam in one direction. When the beam is skewed in this manner with no counter-acting effects, it is more difficult to create high numbers of spots on a mirror.
A majority of these and other prior art arrangements implement matrix ray tracing techniques to simulate the spot pattern before implementation. Commonly, a standard ABCD matrix with thin lens paraxial approximation allows fast simulation, showing a good approximation of the spot positions of standard spherical Herriott calls, especially those with all spots in the same approximate z-plane on a mirror (for example, a single circle spot pattern). More complicated tracers have been developed that use an ABCDEF matrix to account for displaced and tilted surfaces, but preserve paraxial and thin lens approximations.
By continuing to rely on these approximations, however, the various prior art techniques introduce considerable errors into the ray tracing results, particularly after long paths and multiple reflections. For example, at an angle of 5°, the paraxial approximation of θ≈ sin θ is in error by 0.1%, where these errors are not accounted for in these matrix-based calculations.